For a positive trace-class operator C and a bounded operator A, we provide an explicit description of the closure of the orbit-closed C-numerical range of A in terms of those operators submajorized by C and the essential numerical range of A. This generalizes and subsumes recent work of Chan, Li and Poon for the k-numerical range, as well as some of our own previous work on the orbit-closed C-numerical range.

中文翻译：

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闭轨道 C 数值范围的闭性和子优化

对于正迹类算子C和有界算子A ，我们根据由C次重化的那些算子和A的基本数值范围，提供了A的闭轨道C数值范围的闭合的明确描述。这概括并包含了 Chan、Li 和 Poon 最近关于k数值范围的工作，以及我们自己之前在轨道闭合C数值范围上的一些工作。